Problem: Solve for $x$ : $x^2 - 2x - 24 = 0$
Solution: The coefficient on the $x$ term is $-2$ and the constant term is $-24$ , so we need to find two numbers that add up to $-2$ and multiply to $-24$ The two numbers $4$ and $-6$ satisfy both conditions: $ {4} + {-6} = {-2} $ $ {4} \times {-6} = {-24} $ $(x + {4}) (x {-6}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 4) (x -6) = 0$ $x + 4 = 0$ or $x - 6 = 0$ Thus, $x = -4$ and $x = 6$ are the solutions.